PSLE The figure is made up of 6 identical quadrants and 3 identical semicircles. The radius of each quadrant is 12 cm. The unshaded area marked A is enclosed by 2 quadrants and 3 semicircles. (Take π = 3.14)
- Find the perimeter of Z.
- Find the total shaded areas.
(a)
Diameter of the quadrant
= 2 x 12
= 24 cm
Perimeter of 2 quadrants
=
12 x 3.14 x 24
= 37.68 cm
Diameter of the semicircle
= 24 ÷ 3
= 8 cm
Perimeter of 3 semicircles
= 1
12 x 3.14 x 8
= 37.68 cm
Perimeter of Z
= 37.68 + 37.68
= 75.36 cm
(b)
Area of the large circle
= 3.14 x 12 x 12
= 452.16 cm
2
Radius of 1 semicircle
= 8 ÷ 2
= 4 cm
Area of 3 semicircles
= 1
12 x 3.14 x 4 x 4
= 75.36 cm
2 Area of 2 boomerangs
= Area of the rectangle - Area of the semicircle
= 24 x 12 -
12 x 3.14 x 12 x 12
= 288 - 226.08
= 61.92 cm
2 Total shaded areas
= 452.16 - 75.36 - 61.92
= 314.88 cm
2 Answer(s): (a) 75.36 cm; (b) 314.88 cm
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